La méthode MHM pour le modèle élastodynamique de second ordre

The wave propagation phenomena in heterogeneous media is an actual challenging problem to numerical simulation. In today's scenario of increasing computing power and advent of exascale computing, machines provide good environments to obtain solutions to tough problems. However, it is necessary to construct good algorithms that can enjoy this massively parallel computing. The recent Multiscale Hybrid-Mixed (MHM) method is an alternative to be used in such a scenario since it constructs solutions with high-order precision by localizing computations in independent local problems. The final solution is obtained by a post-processing, using solutions of the local problems and the one from a coarse global problem. This work presents the mathematical background of the MHM method for a second-order elastodynamic model in time domain considering highly heterogeneous coefficients. We show several numerical simulations to verify the optimal error convergence of the MHM method and its capacity to deal with heterogeneous three-dimensional media on non-aligned coarse meshes. All the simulations are performed in a hybrid parallel environment and we are able to conclude that the MHM method is a competitive option to handle multiscale wave propagation problems